The use of pairs of relatives who share a trait as the basic unit for mapping genes that influence the trait has great advantages, particularly when the trait of interest is genetically complex or has low or age- dependent penetrance. The aim of the proposed research is to provide statistical methods to aid in the design and analysis of linkage experiments which obtain data delineating regions of identity-by-descent of affected relative pairs along their entire genome. The proposal is motivated by a particular, new laboratory technique: genomic mismatch scanning, which is currently under development in the laboratory of Patrick O. Brown; but the proposed statistical ideas are relevant to the analysis of data obtained from any highly polymorphic, reasonably dense genetic map, e.g., an RFLP linkage map, and can be applied to both Mendelian and quantitative traits. Questions to be addressed are (1) How should regions of enriched identity by descent be identified:? (2) How can one determine the sample size necessary to achieve sufficient power to detect effects of an hypothesized magnitude? (3) When a region or regions of enriched identity by descent have been detected, how should one describe the location and extent of the regions, over which more careful searching should take place? (4) For polygenic traits, how should the contributions of different genes be modeled and estimate? (5) How should data from different kinds of relative pairs be combined in an overall analysis? Similar problems involving homozygosity-by-descent data of consanguineous matings will also be studied. The proposed project involves development of stochastic models by a combination of mathematical analysis an computer simulation, and also analysis of experimental data to validate and refine the models. The important features of the proposed methods are (i) the simultaneous consideration of markers distributed throughout the genome and (ii) exploitation of the mathematical relation between linkage problems and so called "change-point" problems, which have received considerable attention in recent statistical literature.